The present invention relates to a path set-up method and a path set-up system for producing a state transition sequence to reach a target state, and more particularly to a path control method and path set-up method and control system for controlling a path according to a produced path.
State (posture, speed) of a machine may be determined as a position in a phase space and motion of the machine may be determined as a path in the phase space. From time to time, the machine is desired to move from an initial state to a target state. Specific examples follow.
A first example is a case where a humanoid robot loses its balance. An initial state for this case is the posture/speed of the robot immediately after it lost balance, and a target state is a stable posture (upright posture with zero speed).
A second example is a case where an airplane loses balance and stalls. An initial state in this case is a posture/speed immediately after the airplane lost balance, and a target state is a state in which wings and the body are made level and travel straight with constant velocity.
Other examples may be a case wherein a bicycle bumps into a stone to lose balance, which needs be rectified, and a case wherein a car slips.
To control a machine from its initial state into a target state, PID control scheme and potential scheme may be used. But, with these schemes includes a problem that the machine may not work properly depending on the state where the machine lost balance. This problem stems from a fact that with these schemes a broad range of initial state is not permitted in transition of the state of the machine to a target state on a phase space. With the PID control scheme and the potential scheme, the time at which the machine reaches the target state can hardly be defined, and the target state is difficult to reach within a short time.
One way to set up a path planning in the state space includes describing the state transition in the state space as a search tree. In this scheme, a predetermined number of branches are derived from a root or a branch and search is performed for each branch. If the number of branches is N, and depth of the tree is M, the number of branches to be searched is NM. Accordingly, the computation cost for searching all the derived branches becomes huge.
Document 1 identified below proposes a scheme wherein a evaluation function for branches of a search tree is defined and branches are derived from only those branches that are selected according to the evaluation function. With this scheme computation cost may be reduced. But, the evaluation function needs be determined for each object based on expertise of a designer. Search may not be sufficiently performed with some evaluation functions. Accordingly, searching in the state space will have considerable constraints with this scheme.
Conventional schemes of using evaluation functions as well as the above mentioned schemes entail excessively large computation cost (computation time) for production and control of real time path planning.
Document 1: Pedro S. Huang, “Planning For Dynamic Motions Using a Search Tree”, a graduate thesis of Toronto Univ., (1996)